Slow mixing of Glauber dynamics for the hard-core model on regular bipartite graphs
Random Structures & Algorithms
Torpid mixing of local Markov chains on 3-colorings of the discrete torus
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Path coupling using stopping times and counting independent sets and colorings in hypergraphs
Random Structures & Algorithms
A worst-case time upper bound for counting the number of independent sets
CAAN'07 Proceedings of the 4th conference on Combinatorial and algorithmic aspects of networking
On the hardness of counting and sampling center strings
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
A trichotomy theorem for the approximate counting of complex-weighted bounded-degree boolean CSPs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Improved inapproximability results for counting independent sets in the hard-core model
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Guest column: complexity dichotomies of counting problems
ACM SIGACT News
Approximate counting via correlation decay in spin systems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Path coupling using stopping times
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
A dichotomy theorem for the approximate counting of complex-weighted bounded-degree Boolean CSPs
Theoretical Computer Science
Variable ordering for the application of BDDs to the maximum independent set problem
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Journal of Combinatorial Theory Series B
The complexity of approximating bounded-degree Boolean #CSP
Information and Computation
On the Hardness of Counting and Sampling Center Strings
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
The complexity of the counting constraint satisfaction problem
Journal of the ACM (JACM)
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We prove two results concerning approximate counting of independent sets in graphs with constant maximum degree $\Delta$. The first implies that the Markov chain Monte Carlo technique is likely to fail if $\Delta \geq 6$. The second shows that no fully polynomial randomized approximation scheme can exist for $\Delta \geq 25$, unless $\mathrm{RP}=\mathrm{NP}$.